A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.

A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.

Delta Hedging a Short Call using Stocks and Debt

Description

Symbol

Days to maturity (T in days)

60

59

58

57

56

55

Spot price ($)

S

10000

10125

9800

9675

10000

10000

Strike price ($)

K

10000

10000

10000

10000

10000

10000

Risk free cont. comp. rate (pa)

r

0.05

0.05

0.05

0.05

0.05

0.05

Standard deviation of the stock's cont. comp. returns (pa)

σ

0.4

0.4

0.4

0.4

0.4

0.4

Option maturity (years)

T

0.164384

0.161644

0.158904

0.156164

0.153425

0.150685

Delta

N[d1] = dc/dS

0.552416

0.582351

0.501138

0.467885

0.550649

0.550197

Probability that S > K at maturity in risk neutral world

N[d2]

0.487871

0.51878

0.437781

0.405685

0.488282

0.488387

Call option price ($)

c

685.391158

750.26411

567.990995

501.487157

660.982878

?

Stock investment value ($)

N[d1]*S

5524.164129

5896.301781

4911.152036

4526.788065

5506.488143

?

Borrowing which partly funds stock investment ($)

N[d2]*K/e^(r*T)

4838.772971

5146.037671

4343.161041

4025.300909

4845.505265

?

Interest expense from borrowing paid in arrears ($)

r*N[d2]*K/e^(r*T)

0.662891

0.704985

0.594994

0.551449

?

Gain on stock ($)

N[d1]*(SNew - SOld)

69.052052

-189.264008

-62.642245

152.062648

?

Gain on short call option ($)

-1*(cNew - cOld)

-64.872952

182.273114

66.503839

-159.495721

?

Net gain ($)

Gains - InterestExpense

3.516209

-7.695878

3.266599

-7.984522

?

Gamma

Γ = d^2c/dS^2

0.000244

0.00024

0.000255

0.00026

0.000253

0.000255

Theta

θ = dc/dT

2196.873429

2227.881353

2182.174706

2151.539751

2266.589184

2285.1895

In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is NOT correct?

(a) The call option price is expected to be $654.757851.

(b) The stock investment value used for hedging should be $5506.488143, partly funded by $4845.505265 in debt.

(c) The interest expense on the borrowing from the previous day will be $0.663813.

(d) The gain on the stock is zero and the gain on the short call option is $6.225027.